MathDB

Permutations

Source: Junior Olympiad of Malaysia Shortlist 2015 C8

July 17, 2015

combinatorics

Problem Statement

Let

a

be a permutation on

\{0,1,\ldots ,2015\}

and

b,c

are also permutations on

\{1,2,\ldots ,2015\}

. For all

x\in \{1,2,\ldots ,2015\}

, the following conditions are satisfied:
(i)

a(x)-a(x-1)\neq 1

,\\ (ii) if

b(x)\neq x

, then

c(x)=x

,\\
Prove that the number of

a

's is equal to the number of ordered pairs of

(b,c)

.

Back to Problems View on AoPS